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Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models
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Kosmidis, Ioannis and Firth, David (2021) Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models. Biometrika, 108 (1). pp. 71-82. asaa052. doi:10.1093/biomet/asaa052 ISSN 0006-3444.
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Official URL: https://doi.org/10.1093/biomet/asaa052
Abstract
Penalization of the likelihood by Jeffreys’ invariant prior, or a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of models includes logistic regression, where the Jeffreys-prior penalty is known additionally to reduce the asymptotic bias of the maximum likelihood estimator, and models with other commonly used link functions, such as probit and log-log. Shrinkage towards equiprobability across observations, relative to the maximum likelihood estimator, is established theoretically and studied through illustrative examples. Some implications of finiteness and shrinkage for inference are discussed, particularly when inference is based on Wald-type procedures. A widely applicable procedure is developed for computation of maximum penalized likelihood estimates, by using repeated maximum likelihood fits with iteratively adjusted binomial responses and totals. These theoretical results and methods underpin the increasingly widespread use of reduced-bias and similarly penalized binomial regression models in many applied fields.
Item Type: | Journal Article | ||||||||||||
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Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Logistic regression analysis, Mathematical statistics, Mathematical models, Probits, Multivariate analysis | ||||||||||||
Journal or Publication Title: | Biometrika | ||||||||||||
Publisher: | Biometrika Trust | ||||||||||||
ISSN: | 0006-3444 | ||||||||||||
Official Date: | March 2021 | ||||||||||||
Dates: |
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Volume: | 108 | ||||||||||||
Number: | 1 | ||||||||||||
Page Range: | pp. 71-82 | ||||||||||||
Article Number: | asaa052 | ||||||||||||
DOI: | 10.1093/biomet/asaa052 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 8 April 2020 | ||||||||||||
Date of first compliant Open Access: | 13 October 2020 | ||||||||||||
RIOXX Funder/Project Grant: |
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